I've actually had to write an ebook (for content marketing purposes) on growing a company and going from 3 to 9 to 30, and so on. The most interesting thing is the Greiner's Growth Curve as well as Adizes Corporate Lifecycle.

I'll leave the direct link to the pdf here even though it's gated content, so pls downvote.

https://activecollab.com/downloads/GROWTH.pdf